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Lowest zero Conductor Analytic conductor Central character Analytic rank
Degree Bad \(p\) Root analytic conductor Motivic weight Spectral label
Root angle Primitive Origin Exclude origin Self-dual
Arithmetic
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Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim arith $\mathbb{Q}$ self-dual $\operatorname{Arg}(\epsilon)$ $r$ First zero Origin
2-338-13.11-c2-0-0 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.123$ $0$ $0.0605900$ Modular form 338.3.f.k.89.1
2-338-13.11-c2-0-1 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.376$ $0$ $0.399374$ Modular form 338.3.f.l.89.6
2-338-13.11-c2-0-10 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.0457$ $0$ $1.14208$ Modular form 338.3.f.d.89.1
2-338-13.11-c2-0-11 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.120$ $0$ $1.21602$ Modular form 338.3.f.g.89.1
2-338-13.11-c2-0-12 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.0956$ $0$ $1.43106$ Modular form 338.3.f.k.89.4
2-338-13.11-c2-0-13 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.207$ $0$ $1.48177$ Modular form 338.3.f.k.89.3
2-338-13.11-c2-0-14 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.00308$ $0$ $1.51079$ Modular form 338.3.f.j.89.2
2-338-13.11-c2-0-15 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.295$ $0$ $1.69414$ Modular form 338.3.f.f.89.1
2-338-13.11-c2-0-16 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.323$ $0$ $1.78708$ Modular form 338.3.f.l.89.1
2-338-13.11-c2-0-17 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.195$ $0$ $1.81114$ Modular form 338.3.f.l.89.3
2-338-13.11-c2-0-18 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.374$ $0$ $2.13639$ Modular form 338.3.f.k.89.5
2-338-13.11-c2-0-19 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.496$ $0$ $2.15265$ Modular form 338.3.f.c.89.1
2-338-13.11-c2-0-2 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.00308$ $0$ $0.816185$ Modular form 338.3.f.j.89.1
2-338-13.11-c2-0-20 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.454$ $0$ $2.35567$ Modular form 338.3.f.i.89.1
2-338-13.11-c2-0-21 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.419$ $0$ $2.37755$ Modular form 338.3.f.b.89.1
2-338-13.11-c2-0-22 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.370$ $0$ $2.69525$ Modular form 338.3.f.e.89.1
2-338-13.11-c2-0-23 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.304$ $0$ $2.96273$ Modular form 338.3.f.k.89.2
2-338-13.11-c2-0-24 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.204$ $0$ $3.10377$ Modular form 338.3.f.h.89.1
2-338-13.11-c2-0-3 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.292$ $0$ $0.824968$ Modular form 338.3.f.l.89.2
2-338-13.11-c2-0-4 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.204$ $0$ $0.956296$ Modular form 338.3.f.h.89.2
2-338-13.11-c2-0-5 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.404$ $0$ $0.983263$ Modular form 338.3.f.l.89.5
2-338-13.11-c2-0-6 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.125$ $0$ $1.00033$ Modular form 338.3.f.l.89.4
2-338-13.11-c2-0-7 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $0.129$ $0$ $1.01870$ Modular form 338.3.f.a.89.1
2-338-13.11-c2-0-8 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.176$ $0$ $1.11262$ Modular form 338.3.f.k.89.6
2-338-13.11-c2-0-9 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.11 $2.0$ $2$ ✓ ✓ $-0.454$ $0$ $1.11342$ Modular form 338.3.f.i.89.2
2-338-13.2-c2-0-0 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.214$ $0$ $0.121998$ Modular form 338.3.f.a.249.1
2-338-13.2-c2-0-1 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.297$ $0$ $0.152370$ Modular form 338.3.f.i.249.1
2-338-13.2-c2-0-10 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.398$ $0$ $0.981128$ Modular form 338.3.f.l.249.6
2-338-13.2-c2-0-11 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.297$ $0$ $1.17639$ Modular form 338.3.f.i.249.2
2-338-13.2-c2-0-12 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.202$ $0$ $1.41298$ Modular form 338.3.f.d.249.1
2-338-13.2-c2-0-13 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.0133$ $0$ $1.54718$ Modular form 338.3.f.k.249.5
2-338-13.2-c2-0-14 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.340$ $0$ $1.59270$ Modular form 338.3.f.c.249.1
2-338-13.2-c2-0-15 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.488$ $0$ $1.59369$ Modular form 338.3.f.k.249.2
2-338-13.2-c2-0-16 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.0115$ $0$ $1.61840$ Modular form 338.3.f.l.249.3
2-338-13.2-c2-0-17 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.0355$ $0$ $1.71000$ Modular form 338.3.f.g.249.1
2-338-13.2-c2-0-18 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.159$ $0$ $1.73204$ Modular form 338.3.f.j.249.2
2-338-13.2-c2-0-19 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.0478$ $0$ $1.73836$ Modular form 338.3.f.f.249.1
2-338-13.2-c2-0-2 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.486$ $0$ $0.367713$ Modular form 338.3.f.l.249.4
2-338-13.2-c2-0-20 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.285$ $0$ $1.81126$ Modular form 338.3.f.e.249.1
2-338-13.2-c2-0-21 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.171$ $0$ $1.88755$ Modular form 338.3.f.k.249.4
2-338-13.2-c2-0-22 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.452$ $0$ $1.91396$ Modular form 338.3.f.h.249.1
2-338-13.2-c2-0-23 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.232$ $0$ $1.98253$ Modular form 338.3.f.l.249.1
2-338-13.2-c2-0-24 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.253$ $0$ $2.18214$ Modular form 338.3.f.l.249.2
2-338-13.2-c2-0-3 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.452$ $0$ $0.420624$ Modular form 338.3.f.h.249.2
2-338-13.2-c2-0-4 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.246$ $0$ $0.541595$ Modular form 338.3.f.k.249.3
2-338-13.2-c2-0-5 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $0.101$ $0$ $0.551394$ Modular form 338.3.f.k.249.1
2-338-13.2-c2-0-6 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.159$ $0$ $0.766316$ Modular form 338.3.f.j.249.1
2-338-13.2-c2-0-7 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.0761$ $0$ $0.780270$ Modular form 338.3.f.b.249.1
2-338-13.2-c2-0-8 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.328$ $0$ $0.876123$ Modular form 338.3.f.l.249.5
2-338-13.2-c2-0-9 $3.03$ $9.20$ $2$ $2 \cdot 13^{2}$ 13.2 $2.0$ $2$ ✓ ✓ $-0.267$ $0$ $0.978747$ Modular form 338.3.f.k.249.6
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